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								id: 5900f3ce1000cf542c50fee0
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								challengeType: 5
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								title: 'Problem 97: Large non-Mersenne prime'
							 
						 
					
						
							
								
									
										
										
										
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								forumTopicId: 302214
							 
						 
					
						
							
								
									
										
										
										
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								## Description
 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								< section  id = 'description' > 
							 
						 
					
						
							
								
									
										
										
										
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								The first known prime found to exceed one million digits was discovered in 1999, and is a Mersenne prime of the form 2< sup > 6972593< / sup > −  1; it contains exactly 2,098,960 digits. Subsequently other Mersenne primes, of the form 2< sup > < var > p< / var > < / sup > −  1, have been found which contain more digits.
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
										 
									
								 
							
							
								However, in 2004 there was found a massive non-Mersenne prime which contains 2,357,207 digits: 28433×  2< sup > 7830457< / sup > +1.
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								
							 
						 
					
						
							
								
									
										
										
										
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								Find the last ten digits of this prime number.
							 
						 
					
						
							
								
									
										
										
										
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								< / section > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								## Instructions
 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								< section  id = 'instructions' > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
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								## Tests
 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								< section  id = 'tests' > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								```yml
							 
						 
					
						
							
								
									
										
										
										
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								tests:
							 
						 
					
						
							
								
									
										
										
										
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								  -  text: < code > lrgNonMersennePrime()</ code >  should return a number.
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								    testString: assert(typeof lrgNonMersennePrime() === 'number');
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								  -  text: < code > lrgNonMersennePrime()</ code >  should return 8739992577.
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								    testString: assert.strictEqual(lrgNonMersennePrime(), 8739992577);
							 
						 
					
						
							
								
									
										
										
										
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								```
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
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								## Challenge Seed
 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								< section  id = 'challengeSeed' > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								< div  id = 'js-seed' > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								```js
							 
						 
					
						
							
								
									
										
										
										
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								function lrgNonMersennePrime() {
							 
						 
					
						
							
								
									
										
										
										
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								  return true;
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								}
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								
							 
						 
					
						
							
								
									
										
										
										
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								lrgNonMersennePrime();
							 
						 
					
						
							
								
									
										
										
										
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								```
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								< / div > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
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								## Solution
 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								< section  id = 'solution' > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								```js
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								// solution required
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								```
							 
						 
					
						
							
								
									
										
										
										
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								< / section >